{
  "id": "0802.4076",
  "version": "v3",
  "published": "2008-02-27T20:10:11.000Z",
  "updated": "2009-08-10T19:22:18.000Z",
  "title": "Notes on Measure and Integration",
  "authors": [
    "John Franks"
  ],
  "comment": "This version corrects a few typos. An expanded version of this text has been published as \"A (Terse) Introduction to Lebesgue Integration\" as vol. 48 of the A.M.S. Student Mathematical Library",
  "categories": [
    "math.CA"
  ],
  "abstract": "This text grew out of notes I have used in teaching a one quarter course on integration at the advanced undergraduate level. My intent is to introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to investigate the standard convergence theorems and a brief introduction to the Hilbert space of $L^2$ functions on the interval. The actual construction of Lebesgue measure and proofs of its key properties are relegated to an appendix. Instead the text introduces Lebesgue measure as a generalization of the concept of length and motivates its key properties: monotonicity, countable additivity, and translation invariance.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-08-10T19:22:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integration",
      "lebesgue measure",
      "standard convergence theorems",
      "translation invariance",
      "lebesgue integral"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.4076F"
    }
  }
}